Finite Group DatabasebetaFinite Group Databasebeta| order | 9496 |
| automorphism | Aut(G) order 11262256 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2374 |
| unambiguous semidirect product | C1187⋊Q8 |
| Sylow | C1187 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1187 |
| commutator, socle, prime radical, cosocle | C2×C1187 | C22 |
| Fitting | C4×C1187 | C2 |
| hypercenter | C4 | D1187 |
| hypocenter | C1187 | Q8 |
| LCS | G ▷ C2×C1187 ▷ C1187 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1187|a^2=c,b^2=c,b^a=bc,d^b=d^11862377 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34039542, #34039543, #34039544, … |
| maximal normal subgroup of | #34039542, #34039543, #34039544, … |
| maximal quotient of | Dic1187⋊C4, C4⋊Dic1187, C2×Dic2374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9496, 11);